Solve the below problem:
Q: The lengths of the minor and major axes are used to summarize dust particles that are approximately elliptical in shape. Let X and Y denote the lengths of the minor and major axes (in micrometers), respectively. Suppose that fX (x) = exp(-x),0 (a) That fY|x (y) is a probability density function for any value of x.
(b) P(X
(c) Joint probability density function fXY (x, y).
(d) Conditional probability density function of X given Y = y.
(e) P(Y
(f) E(Y | X = 1
)(g) P(X (h) P(Y
(i) c such that P(Y)
(j) Are X and Y independent?